Question: Solve for $x$ and $y$ using elimination. ${5x+5y = 55}$ ${6x-2y = -6}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $2$ and the bottom equation by $5$ ${10x+10y = 110}$ $30x-10y = -30$ Add the top and bottom equations together. $40x = 80$ $\dfrac{40x}{{40}} = \dfrac{80}{{40}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {5x+5y = 55}\thinspace$ to find $y$ ${5}{(2)}{ + 5y = 55}$ $10+5y = 55$ $10{-10} + 5y = 55{-10}$ $5y = 45$ $\dfrac{5y}{{5}} = \dfrac{45}{{5}}$ ${y = 9}$ You can also plug ${x = 2}$ into $\thinspace {6x-2y = -6}\thinspace$ and get the same answer for $y$ : ${6}{(2)}{ - 2y = -6}$ ${y = 9}$